%   ORIGINAL: 'h4/thm/list/EL_LENGTH_dropWhile_REVERSE_'
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Goal: !P ls k. 'h4/const/arithmetic/<=' ('h4/const/list/LENGTH' ('h4/const/list/dropWhile' P ('h4/const/list/REVERSE' ls))) k /\ 'h4/const/prim_rec/<' k ('h4/const/list/LENGTH' ls) ==> P ('h4/const/list/EL' k ls)
%   PROCESSED
% Assm ['HL_TRUTH']: T
% Assm ['HL_FALSITY']: ~F
% Assm ['HL_BOOL_CASES']: !t. (t <=> T) \/ (t <=> F)
% Assm ['HL_EXT']: !f g. (!x. happ f x = happ g x) ==> f = g
% Goal: !P ls k. 'h4/const/arithmetic/<=' ('h4/const/list/LENGTH' ('h4/const/list/dropWhile' P ('h4/const/list/REVERSE' ls))) k /\ 'h4/const/prim_rec/<' k ('h4/const/list/LENGTH' ls) ==> happ P ('h4/const/list/EL' k ls)
fof('HL_TRUTH', axiom, p(s(bool,'T'))).
fof('HL_FALSITY', axiom, ~ (p(s(bool,'F')))).
fof('HL_BOOL_CASES', axiom, ![T]: (s(bool,T) = s(bool,'T') | s(bool,T) = s(bool,'F'))).
fof('HL_EXT', axiom, ![V_3f12844,V_3f12840]: ![F, G]: (![X]: s(V_3f12840,happ(s(fun(V_3f12844,V_3f12840),F),s(V_3f12844,X))) = s(V_3f12840,happ(s(fun(V_3f12844,V_3f12840),G),s(V_3f12844,X))) => s(fun(V_3f12844,V_3f12840),F) = s(fun(V_3f12844,V_3f12840),G))).
fof('h4/thm/list/EL_LENGTH_dropWhile_REVERSE_', conjecture, ![A]: ![P, Ls, K]: ((p(s(bool,'h4/const/arithmetic/<='(s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),'h4/const/list/dropWhile'(s(fun(A,bool),P),s('h4/type/list/list'(A),'h4/const/list/REVERSE'(s('h4/type/list/list'(A),Ls))))))),s('h4/type/num/num',K)))) & p(s(bool,'h4/const/prim_rec/<'(s('h4/type/num/num',K),s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),Ls))))))) => p(s(bool,happ(s(fun(A,bool),P),s(A,'h4/const/list/EL'(s('h4/type/num/num',K),s('h4/type/list/list'(A),Ls)))))))).
